Hydrodynamic limits for singular SPDEs

Hydrodynamic limits describe the macroscopic behaviour of random systems. In this talk, I will discuss them for singular stochastic PDEs, starting with the stochastic Burgers equation. I will explain why standard pathwise methods are not sufficient, and how probabilistic tools such as energy solutions and relative entropy can help. Finally, I will discuss current bottlenecks and future directions towards other singular SPDEs.